Mr Key told RNZ today National was polling what it was on election night last November.
"The Government faces lots and lots of challenges and, in fact, if you look at the programme we're undertaking and where we're taking New Zealand, the one thing I came away from the European trip was thinking New Zealand's in pretty good shape in relation to all these other countries."
The poll of 1000 eligible voters was conducted between May 29 and June 6, at the height of the Government's Budget crisis over its plan for increased class sizes, which it eventually dumped on Thursday.
Mr Key said there would always be a little bit of push-back to reform from time to time.
"In terms of education, fundamentally there that is a debate about what is the right step forward to produce the best outcome for our kids. What the general advice that we've had has been that after a long build-up of more teachers, the question is whether the next best dollar can be spent improving the quality of the 52,000 teachers and principals."
It was better to accept that parents did not accept changes in class sizes, than go through months and months of industrial action, he said.
"Sometimes it's just better to say, well we accept that people don't feel comfortable with that particular route and take another route to achieve the same outcomes."
But Mr Shearer, speaking to Firstline this morning, said the overall trend showed that Labour's support was increasing and that was positive for both him and the party.
"I think what you've got is a series of incidents, like the classroom sizes type of activity going on, but there's also other things going on behind the scenes, and I think people are getting concerned about as well.''
Mr Shearer said it would take time for the public to get used to him and where he stood, and it was positive to see the overall trend line moving up.
"So we started off at 27 per cent for the Labour result at the election, and we're going about, up to about 33 [per cent] now six months later so the trend line is going in the right direction, and myself I'm going slowly in the right direction as well."
The poll has a margin of error of 3.1 per cent.